TY - JOUR
T1 - On the General Algebraic Inverse Eigenvalue Problems
AU - Zhang , Yuhai
JO - Journal of Computational Mathematics
VL - 4
SP - 567
EP - 580
PY - 2004
DA - 2004/08
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10306.html
KW - Linear algebra, Eigenvalue problem, Inverse problem.
AB - <p style="text-align: justify;">A number of new results on sufficient conditions for the solvability and numerical algorithms of the following general algebraic inverse eigenvalue problem are obtained: Given $n+1$ real $n\times n$ matrices $A=(a_{ij}),A_k=(a_{ij}^{(k)})(k=1,2,\cdots,n)$ and $n$ distinct real numbers $\lambda_1,\lambda_2,\cdots,\lambda_n,$ find $n$ real number $c_1,c_2,\cdots,c_n$ such that the matrix $A(c)=A+\sum\limits_{k=1}^{n}c_k A_k$ has eigenvalues $\lambda_1,\lambda_2,\cdots,\lambda_n.$</p>